Under the same load, wire $A$ having length $5.0\,m$ and cross section $2.5 \times 10^{-5}\,m ^2$ stretches uniformly by the same amount as another wire $B$ of length $6.0\,m$ and a cross section of $3.0 \times 10^{-5}\,m ^2$ stretches. The ratio of the Young's modulus of wire $A$ to that of wire $B$ will be

The dimensions of four wires of the same material are given below. In which wire the increase in length will be maximum when the same tension is applied

A cylindrical wire of radius $1\,\, mm$, length $1 m$, Young’s modulus $= 2 × 10^{11} N/m^2$, poisson’s ratio $\mu = \pi /10$ is stretched by a force of $100 N$. Its radius will become

A steel rod has a radius of $20\,mm$ and a length of $2.0\,m$. A force of $62.8\,kN$ stretches it along its length. Young's modulus of steel is $2.0 \times 10^{11}\,N / m ^2$. The longitudinal strain produced in the wire is $……….\times 10^{-5}$

When a certain weight is suspended from a long uniform wire, its length increases by one  $cm$. If the same weight is suspended from another wire of the same material and length  but having a diameter half of the first one, the increase in length will be ……… $cm$